A particle is found to be at rest when seen from a frame `S_(1)` and moving with a constant velocity when seen from another frame `S_(2)`
(a) Both the frames are inertial
(b) Both the frames are non inertial
(c ) `S_(1)` is inertial and `S_(2)` is non inertial
(d) `S_(1)` is non inertial and `S_(2)` is inertial

Options

A. a, b are true
B. c, d are true
C. b, c are true
D. a, d are true

Answer

To solve the problem, we need to analyze the motion of a particle as observed from two different frames of reference, \( S_1 \) and \( S_2 \).

### Step-by-step Solution:

1. **Understanding the Problem**:
- A particle is at rest in frame \( S_1 \).
- The same particle is moving with a constant velocity in frame \( S_2 \).

2. **Analyzing Frame \( S_1 \)**:
- Since the particle is at rest in frame \( S_1 \), we can conclude that frame \( S_1 \) is an inertial frame. In an inertial frame, objects either remain at rest or move at a constant velocity unless acted upon by a force.

3. **Analyzing Frame \( S_2 \)**:
- The particle is observed to be moving with a constant velocity in frame \( S_2 \). For this to happen, frame \( S_2 \) must be moving relative to frame \( S_1 \) with some velocity.
- If \( S_2 \) is moving with a constant velocity relative to \( S_1 \), then it is also an inertial frame because it does not accelerate.

4. **Conclusion**:
- Since both frames \( S_1 \) and \( S_2 \) are inertial (neither is accelerating), we can conclude that both frames are inertial frames.
- Therefore, the correct answer is option (a): Both frames are inertial.

### Final Answer:
**(a) Both the frames are inertial.**